Method of production planning

ABSTRACT

For planning a production plan which satisfies a plural number of target values of management indices, upon calculating out production amount, supply amount and/or transportation means of plural products, various kinds of target values of management indices and estrangement values thereof are set into restriction conditions when those restriction conditions are formulated into a linear programming problem, and then feasible production plan is calculated out, so that the estrangement between the management indices being calculated from executable solutions of the above-mentioned linear programming problems and the target values thereof comes to be minimal.

FIELD OF THE INVENTION

[0001] The present invention relates to a method for production planningwith using a linear programming method. The production plan in thisspecification indicates or means a plan, relating to productionactivity, from supply of materials until transportation to a productionpoint (or a base) and/or to a marketing point.

BACKGROUND OF THE INVENTION

[0002] In the manufacturing industry, upon the basis of sales planningfrom the marketing points, there are planned a supply amount ofmaterials and/or a production amount, as well as transportation means,being feasible under the restriction conditions upon the productioncapability and the term and amount of supply of materials. In recentyears, the supply point of materials, the production point, themarketing point have been expanded not only domestically, but alsoabroad, and it is possible to select a plural number of the supplypoints, production points, and the marketing points, with regard to onekind or sort of the products. For example, regarding a product A, theremay be a method, in which the materials are supplied from Asia so as tobe fabricated in Japan, and another way in which they are supplied inJapan so as to be fabricated in U.S.A., etc.

[0003] Several methods are proposed, in each of which the productionplan forming such the production mode is made up with using a linearprogramming method. For example, in NIKKEI DIGITAL ENGINEERING (Decemberof 1998), there is introduced a planning method for production plan, inwhich, under the restriction conditions of production capability and/oramounts of parts supply, while making a production time, a setup time,the maximum past due, and the maximum total past due as objectivefunctions, the management indices, such as, the sales profit maximum,the average inventory minimum, observance of due date, effectiveoperation, etc., are made minimal, respectively. Grade or rank of theeach object is set in the priority, by giving weights thereon.

[0004] In case of using the management indices as the objectivefunctions, it is difficult to bring the plural number of the managementindices at the “minimum (or maximum)”, at the same time. For example,when setting the management index, “total past due” according to theconventional art at the minimum, due to the mechanism of the linearprogramming, the production plans are made up in an order of swiftnessin their delivery times, regardless of the kinds thereof, therefore thesetup time does not necessarily come to be the minimum. This is becausethose management indices have a relationship of so-called trade-off(negative correlation) between them. For the indices being in such therelationship as the trade-off, it is sufficient that both those valuescome to be values being desirable for a person in charge of planning theproduction plan, i.e., a person who can decides one's mind, but not beminimized (maximized) at the same time. The desirable value is a numeralvalue which can be given in advance, i.e., the “value” at which thetarget is set by the person in charge of planning the production plan,such as, “it is desired that the inventory should be at ¥100,000” or thelike, or is a ranges in values, such as “it is desired that theinventory should be less than ¥200,000”. According to the conventionalart, since parameters being changeable for approaching the managementindices to those target values (or within the ranges) are only theweights, therefore, for the purpose of approaching them to the targetvalues, it is necessary to know the numeral values, at which the weightsare to be set, by experiences. For the purpose of knowing them byexperiences, it is necessary to solve a problem of the linearprogramming while adjusting the weights, as well as to repeat theoperation of confirming the values of those management indices,therefore it sometimes necessitates times so as to make up theproduction plan.

[0005] When it is delayed in the planning of the production plan, thetimings for starting the supply of materials, for preparation ofproduction, and also for supplying the products onto the marketingpoints are delayed or postponed, it is impossible to deliver theproducts to the customers earlier than competitors.

SUMMARY OF THE INVENTION

[0006] An object of the present invention is, for dissolving such theproblems as mentioned above, to provide a method of production planning,wherein the values or ranges to be achieved at the lowest are taken intothe consideration, for each of the management indices, when formulatingthe restriction conditions into the linear programming problem.

[0007] Another object of the present invention is to provide a method ofproduction planning, wherein, in relation to the management indices forevaluation of the production plan, the condition of restriction isproduced by means of the combination of at least one of theabove-mentioned management indices, and by adding cash which theproduction activity produces and/or an efficiency, at which theproduction activity produces the cash, other than inventory, profit,sales, cost, a rate of operation (or the working ratio), and afulfilling rate on demands from the marketing points, etc.

[0008] For achieving the object mentioned above, according to thepresent invention, there is provided a method of production planning,comprising steps of: putting a relationship between a target value of apredetermined management index and an estrangement value therefrom intorestriction condition, when formulating the restriction condition into alinear programming problem; and calculating out a feasible productionplan, so that the estrangement between the predetermined managementindex and the target value thereof, being calculated from an executablesolution of the linear programming problem, comes to be minimal.

[0009] Also, for achieving the object mentioned above, in the method ofproduction planning, as is defined in the above, wherein the managementindex is a combination of at least one or more of inventory, profit,sales, cost, a rate of operation, a fulfilling rate on demands frommarketing point, cash which production activity produces, and anefficiency at which the production activity produces the cash.

[0010] Also, for achieving the object mentioned above, in the method ofproduction planning, as is defined in the above, wherein the targetvalue of the management index is set to be equal to, greater or lessthan that, or maximal or minimal, with respect to a numerical valueappointed.

[0011] Also, for achieving the object mentioned above, in the method ofproduction planning, as is defined in the above, wherein the productionamount and/or the supply amount and/or the transport means is/arecalculated out by repeating steps of: setting the target value of themanagement index through an input means, solving the linear programmingproblem in a calculation means, displaying a result thereof on a displaymeans, and again, changing the restriction condition stored in a memorymeans upon receipt of change in the target value of the management indexthrough the input means, solving the linear programming problem, therestriction condition of which is changed, in the calculation means, anddisplaying the result thereof on the display means.

[0012] Also, for achieving the object mentioned above, by means of amemory medium storing programs for executing the method of productionplanning of the present invention, it is possible to provide the methodto sections being in necessary thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013]FIG. 1 is a view of showing flows of storage into a warehouse anddelivery therefrom;

[0014]FIG. 2 is a view of showing a relationship between products andcash;

[0015]FIG. 3 is a view of showing flows of processes until planning ofthe production plan;

[0016]FIG. 4 is a view of showing the bill of materials, in an exampleof the planning of the production plan;

[0017]FIG. 5 is a view of showing flows of supply-production-sales, inthe example of the planning of the production plan;

[0018]FIG. 6 is a view of showing information relating to transportroute and transport means, in the example of the planning of theproduction plan;

[0019]FIG. 7 is a view of showing information relating to a productionpoint, in the example of the planning of the production plan;

[0020]FIG. 8 is a view of showing information relating to a supplypoint, in the example of the planning of the production plan;

[0021]FIG. 9 is a view of showing a part of the production plan, whichis planned in an exercise 1;

[0022]FIG. 10 is a view of showing a part of the production plan, whichis planned at a first (1^(st)) time in an exercise 2;

[0023]FIG. 11 is a view of showing management indices of the productionplan, which is planned at the first (1^(st)) time in the exercise 2;

[0024]FIG. 12 is a view of showing a part of the production plan, whichis planned at a second (2^(nd)) time in the exercise 2;

[0025]FIG. 13 is a view of showing the management indices of theproduction plan, which are planned at the second time in the exercise 2;

[0026]FIG. 14 is a view of showing the management indices of theproduction plan, in a form of a radar chart, which is planned at thefirst (1^(st)) time in the exercise 2;

[0027]FIG. 15 is a view of showing the management indices of theproduction plan, in a form of a bar graph, which is planned at the first(1^(st)) time in the exercise 2;

[0028]FIG. 16 is a view of showing the management indices of theproduction plan, in a form of the radar chart, which is planned at thesecond (2^(nd)) time in the exercise 2; and

[0029]FIG. 17 is a view of showing the management indices of theproduction plan, in a form of the bar graph, which is planned at thesecond (2^(nd)) time in the exercise 2.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0030] In a method of production plan according to the presentinvention, upon basis of sales plan or schedule from a s(s), targetvalues on management tactics, such as, storage, profit, sales, cost, therate of operation, the fulfillment rate on amount of demands from themarketing points, cash which the production activity creates orproduces, an efficiency, at which the production activity creates orproduces the cash, etc., are set to be the restriction conditions, inaddition to production capability at each of the points ortransportation capability between the points, and the restriction onparts. And, they are formulated into a linear programming problem(s) bysetting them into objective functions, so that the estrangement ordiscrepancies from the above-mentioned target values are minimized.

[0031] The method of production plan according to the present inventionwill be explained, by taking a production activity of fabricating orassembling semi-products from plural parts, and a activity of assemblingor fabricating products from the plural semi-products and/or parts, asexamples.

[0032] First, in determining the restriction upon parts and/or therestriction upon production capability, by paying attention onto thestorage of the parts, the semi-products and/or the products, those areconsidered to be in warehouse(s), and flows of storage into thewarehouse and of delivery from it are made into models, in each of theterms, without discrimination among those parts, semi-products and/orproducts. The flows of storage into the warehouse and of delivery fromit are shown in FIG. 1. Orders for the parts are given to partsmanufacturers (supply points) 101, and they are supplied after adelivery lead time, thereby being stored into the warehouses 102 asinventory of the parts. The warehouses 102 for the parts are consideredto be located at parts supply points, for simplicity thereof in themodels, however, in practice, it does not matter that they are locatedanywhere. The semi-products are manufactured, by delivering thenecessary parts from warehouse 102 of the parts to a production point104 in need thereof, after a transportation lead time 103, respectively,in a process 105 of the point and they are stored into the warehouse106, thereby becoming inventory of semi-products. The products aremanufactured, by delivering necessary parts and/or the semi-productsfrom the respective warehouses 102 and 106 thereof to a production point108 in need thereof, after a transportation lead time 107, in a process109 of the point, and they are stored into the warehouse 110, therebybecoming inventory of products. The inventory of products is deliveredby taking the transport lead time into the consideration, so as to bewithin the due date to the marketing points.

[0033] Paying attention onto the storage and delivery into/from thewarehouse, all of the parts, the semi-products and the products takeflows, such as, storage into the warehouse→the warehouse→delivery fromthe warehouse, and the quantities of respective ones are depending uponone another, in the name of the same item. Also, the quantity ofdelivery for each item can be determined uniquely, by the quantity ofstorage of the item in need thereof, and the quantity of storage intoeach point for every term can be determined, in particular that of thesemi-products and/or the products can be determined, by an amount ofproduction in the process of the production point, while that of theparts can be determined by released order from the parts manufacturers(i.e., an estimated amount of the storage into the warehouse(s)).

[0034] Namely, the processes from the supply of parts until the deliveryto the marketing points can be formulated into a linear programmingproblem, by combining those processes, i.e., the storage→thewarehouse→the delivery of the each item.

[0035] First of all, assuming that:

[0036] T: the term of a target for planning (term);

[0037] N: the kinds or sorts of the products;

[0038] M: the kinds or sorts of the semi-products;

[0039] B: the kinds or sorts of the parts;

[0040] R: the number of the supply points (=the number of the partsmanufacturers);

[0041] P: the number of the production points (=the number of theprocesses);

[0042] S: the number of the marketing points; and

[0043] E: the number of the transportation means,

[0044] where appendices are set to be indicated by the follow equation:

[0045] (Eq. 1): Appendices

[0046] t: the term at random (t=1,2, . . . , T);

[0047] i: the items (N pieces of the products, M pieces of intermediateparts, and B pieces of the parts) (i=1,2, . . . , N+M+B);

[0048] r: the parts manufacturer at random (r=p=1,2, . . . , R);

[0049] p,p′: the processes of the production points at random(p(=p′)=R+1,R+2, . . . , R+P+S);

[0050] s: the marketing points at random (s=p=R+P+1,R+P+2, . . . ,R+P+S); and

[0051] e: the transport means (e=1,2, . . . , E)

[0052] The following constants can be listed up, to be necessary whenplanning the production plans for the 1^(st) term to T^(th) term:

[0053] (Eq. 2): Constants

[0054] I_(i0) ^(p): the amount of inventory in the process p of the itemi at the end of 0^(th) term (at the head of 1^(st) term)

[0055] (i=1,2, . . . , N+M+B)

[0056] (p=R+1,R+2, . . . , R+P));

[0057] LT_(i) ^(p): the lead time of the item i, from casting intoprocess up to storage into the warehouse in the process p,

[0058] (i=1,2, . . . , N+M+B)

[0059] (p=R+1,R+2, . . . , R+P));

[0060] LT_(ie) ^(pp′): the transport lead time of the item i, from theprocess p to the process p′, via the means e,

[0061] (i=1,2, . . . , N+M+B)

[0062] (e=1, . . . , E)

[0063] (p=1,2, . . . , R+P,p′=R+1,R+2, . . . , R+P+S);

[0064] BM_(ij): required amount of the items j being necessary forproducing the item i, by one unit,

[0065] (i=1,2, . . . , N+M)

[0066] (j=N+1,N+2, . . . , N+M+B);

[0067] BMS_(ij): required amount of the items j being necessary forproducing the item i, by one unit (1 layer),

[0068] (i=1,2, . . . , N)

[0069] (j=N+M+1,N+M+2, . . . , N+M+B);

[0070] W_(it) ^(pp′): the amount of the released orders and/or work inprocess of the item i,, into the warehouse from the process p to theprocess p′,

[0071] (i=1,2, . . . , N+M+B)

[0072] (p=R+1,R+2, . . . , R+P)

[0073] (t=1,2, . . . , T);

[0074] WF_(i) ^(pp′): the estimated amount of the released orders and/orwork in process of the item i, into the warehouse from the process p tothe process p′, after T+1^(th) term,

[0075] (i=N+M+1,2, . . . , N+M+B)

[0076] (p=R+1,R+2, . . . , R+P);

[0077] C_(t) ^(p): operable time at the process p in the t^(th) term,

[0078] (p=R+1,R+2, . . . , R+P)

[0079] (t=1,2, . . . , T);

[0080] K_(i) ^(p): operable time at the process p for the item i,

[0081] (i=1,2, . . . , N+M+B)

[0082] (p=R+1,R+2, . . . , R+P);

[0083] D_(it) ^(s): estimated amount of sales of the item i in thet^(th) term from the marketing points s,

[0084] (s(=p)=R+P+1,R+P+2, . . . , R+P+S)

[0085] (i=1,2, . . . , N)

[0086] (t=1,2, . . . , T);

[0087] PR_(i) ^(s): selling price of the item i to s,

[0088] (s(=p)=R+P+1,R+P+2, . . . , R+P+S)

[0089] (i=1,2, . . . , N);

[0090] PM_(i) ^(p): standard cost,

[0091] (p=R+1,R+2, . . . , R+P);

[0092] PP_(i) ^(r): unit price when supplying the item i at the partsmanufacturer r,

[0093] (i=N+M+1, . . . , N+M+B)

[0094] (r(=p)=1,2, . . . , R);

[0095] PP_(i) ^(p): production cost of the item i at the process p,

[0096] (i=1,2, . . . , N+M+B)

[0097] (p=R+1,R+2, . . . , R+P);

[0098] PO^(p): over time cost at the process p,

[0099] (p=R+1,R+2, . . . , R+P);

[0100] IR_(i) ^(s): : a rate of interest for the t^(th) term on the itemon the process p,

[0101] (p=1, . . . , R+P)

[0102] (i=1,2, . . . , N+M+B)

[0103] (t=1,2, . . . , T);

[0104] Q_(ie) ^(pp′): unit transport cost of the item i from the processp up to p′ via the transport means e,

[0105] (i=1, 2, . . . , N+M+B)

[0106] (e=1 . . . , E)

[0107] (p=1,2, . . . , R+P, p′=R+1,R+2, . . . , R+P+S);

[0108] DC_(et) ^(pp′): capable capacity of transportation in the t^(th)term from the process p to p′ via the transport means e,

[0109] (e=1, . . . , E)

[0110] (p=1,2, . . . , R+P, p′=R+1,R+2, . . . , R+P+S);

[0111] V_(i): transport capacity per a unit of the item i,

[0112] (i=1,2, . . . , N+M+B);

[0113] FC: fixed cost; and

[0114] BMM_(ij): required amount of the parts j being necessary forproducing a half product i by one unit (1 layer)

[0115] The variables are set as follows:

[0116] (Eq. 3): Variables

[0117] I_(it) ^(p): amount of inventory of the item i at the end of thet^(th) term at the process p,

[0118] (i=1,2, . . . , N+M+B),

[0119] (t=1,2, . . . , T)

[0120] (p=r+1, 2, . . . , R+P);

[0121] R_(it) ^(p): amount of storage into the warehouse of the item iat the process p in the t^(th) term (except for the released orders andthe work in process),

[0122] (i=1,2, . . . , N+M+B),

[0123] (t=1,2, . . . , T),

[0124] (p=r+1,2, . . . , R+P),

[0125] however, R_(it) ^(p)≧0;

[0126] U_(iet) ^(pp′): amount of delivery of the item i from thewarehouse, from the process p to p′ via the means e in the t^(th) term,

[0127] (i=N+1,N+2, . . . , N+M+B),

[0128] (t=1,2, . . . , T),

[0129] (p=1,2, . . . , R+P+S),

[0130] however, U_(iet) ^(pp′)≧0;

[0131] X_(it) ^(s): distribution amount of the item i to the marketingpoints s in the t^(th) term,

[0132] (s=(p=)R+P+1,R+P+2, . . . , R+P+S)

[0133] (i=1,2, . . . , N)

[0134] (t=1,2, . . . , T)

[0135] however, X_(it) ^(s)≧0; and

[0136] CO_(t) ^(p): over time at the process p in the t^(th) term

[0137] However, the amount R of storage into the warehouse in relationwith the parts indicates the supply amount of the parts which will begenerated newly (except for the released orders), while the amount R ofstorage into the warehouse in relation with the semi-products and/or theproducts indicates the production amount at each of the productionpoints which will be generated newly (except for the amount of the workin process).

[0138] <Restriction Condition 1>

[0139] Since the inventory of the item i at the point p in the t^(th)term is at an amount, which can be obtained by subtracting the deliveryin the t^(th) term from the amount obtained by adding the storage in thet−1^(th) term and the expectation of the storage in the t−1^(th) term tothe inventory in the t−1^(th) term (the released orders or the work inprocess), it comes to be as follows:(Eq. 4): Restriction Condition 1                                                                 $I_{it}^{p} = {I_{{it} - 1}^{p} + R_{it}^{p} + {\sum\limits_{p^{''} = 1}^{R + P}W_{it}^{p^{''}p}} - {\sum\limits_{e = 1}^{E}{\sum\limits_{p^{\prime} = 1}^{p + S}U_{iet}^{{pp}^{\prime}}}}}$$\begin{matrix}{( {{i = 1},2,\ldots \quad,{N + M + B}} )\quad ( {{{p( {= p^{\prime}} )} = {R + 1}},{R + 2},\ldots \quad,{R + P}} )} \\{( {{t = 1},2,\ldots \quad,T} ),( {{e = 1},2,\ldots \quad,E} )}\end{matrix}$

[0140] This is common for the products, the semi-products, and the partsthereof.

[0141] <Restriction Condition 2>

[0142] The amount of the delivery of the item j in the t^(th) term comesto “the expectation of storage×the required amount of the item j” of theitem i following thereto (the item being produced by making the j as theparts thereof). However, since the item j is the semi-products or theparts, and since the item i is the parts or the semi-products, thereforethe following relationship is established:(Eq. 5): Restriction Condition 2                                                                  ${\sum\limits_{\underset{t - {LT}_{ie}^{{pp}^{\prime} \geq 1}}{p}}{\sum\limits_{e}U_{{jet} - {LT}_{ie}^{{pp}^{\prime}}}^{{pp}^{\prime}}}} = {\sum\limits_{i = \underset{{t + {LT}_{i}^{p}} \leq T}{1}}^{N + M}{{BM}_{ij} \cdot R_{i{({t + {LT}_{i}^{p^{\prime}}})}}^{p^{\prime}}}}$$\begin{matrix}{( {{j = {N + 1}},\ldots \quad,{N + M + B}} )\quad ( {{{p( {= p^{\prime}} )} = {R + 1}},{R + 2},\ldots \quad,{R + P}} )} \\{( {{t = 1},2,\ldots \quad,T} )\quad ( {{e = 1},2,\ldots \quad,E} )}\end{matrix}$

[0143] <Restriction Condition 3>

[0144] The storage amounts of the products and the semi-products i andthe expectation amounts thereof are restricted by the operable time atthe process for the production thereof. Namely, since the products andthe semi-products i which will be produced at the process p in thet^(th) term cannot be produced beyond the operable time which theprocess p has in the t^(th) term, the storage amount of i comes to be asfollows:

[0145] (Eq. 6): Restriction Condition 3${{\sum\limits_{i = 1}^{N + M}\{ {K_{i}^{p} \cdot ( {R_{it}^{p} + {\sum\limits_{p^{\prime} = {R + 1}}^{R + P}W_{it}^{{pp}^{\prime}}}} )} \}} \leq C_{t}^{p}}{( {{p = {R + 1}},\ldots \quad,P} ),( {{i = {N + 1}},\ldots \quad,{N + M + B}} )}$(t = 1, 2, …  , T)  (e = 1, 2, …  , E)

[0146] In case of taking the over times into the consideration, it maybe replaced by the following:

[0147] (Eq. 7): Restriction Condition 4${\sum\limits_{i = 1}^{N + M}\{ {K_{i}^{p} \cdot ( {R_{it}^{p} + {\sum\limits_{p^{\prime} = {R + 1}}^{R + P}W_{it}^{{pp}^{\prime}}}} )} \}} \leq {C_{t}^{p} + {CO}_{t}^{p}}$(p = R + 1, …  , P), (i = N + 1, …  N + M + B)(t = 1, 2, …  , T)  (e = 1, 2, …  , E)

[0148] In case where there is an upper limit for the over time, thefollowing restriction condition is added by setting the upper limit ofover time at the process p in the t^(th) term (a constant) to beOpt≦OMAX(p,t):

[0149] (Eq. 8): Restriction Condition 5

Opt≦OMAX(p,t),

[0150] (p=R+1, . . . , P),

[0151] (i=N+1, . . . N+M+B)

[0152] (t=1,2, . . . , T)

[0153] <Restriction Condition 4>

[0154] For the storage of the item i in the t^(th) term, the delivery ofthe parts which will be used for the item (or the order in case of theparts) is generated before the transport lead time+ the lead time untilthe storage after the production thereof (or supply lead time in case ofthe parts), however if it occurred in the past term, the production (orthe order) is impossible, therefore the following is established:

[0155] (Eq. 9): Restriction Condition 4

R_(it) ^(p)=0

[0156] (i=1, . . . N+M+B)

[0157] (p(=p′)=R+1,R+2, . . . , R+P)

[0158] (t|t−LT_(i) ^(p)≦0,t=1, . . . . , T,i∈B)

[0159] <Restriction Condition 5>

[0160] Since the delivery of the products i is distributed to themarketing points, the following is established:

[0161] (Eq. 10): Restriction Condition 5${\sum\limits_{p}{\sum\limits_{e}U_{{ie}{({t - {LT}_{ie}^{ps}})}}^{ps}}} = {{x_{it}^{s}( {{s = {R + P + 1}},{R + P + 2},\ldots \quad,{R + P + S}} )}\quad ( {{p = {R + 1}},{R + 2},\ldots \quad,{R + P}} )}$(i = 1, 2, …  , N)  (t = 1, 2, …  , T)

[0162] <Restriction Condition 6>

[0163] Since the amount to be distributed to the marketing points doesnot go beyond the expectation amount of sales, the following isestablished:(Eq. 11): Restriction Condition 6                                                        D_(it)^(s) ≥ x_(it)^(s)  (i = 1, …  , N), (s ∈ S)  (t = 1, …  , T)

[0164] <Restriction Condition 7>

[0165] The amount of delivery of the item is restricted upon atransportable amount. Since the amount to be delivered from the processp to the process p′ in the t^(th) term through the transport means edoes not go beyond the transport capability, the following isestablished: (Eq. 12): Restriction Condition 7  ${{\sum\limits_{i = 1}^{N + M + B}\{ {V_{i} \cdot U_{iet}^{{pp}^{\prime}}} \}} \leq {{{DC}_{et}^{{pp}^{\prime}}( {{p = 1},\ldots \quad,{R + P}} )}\quad ( {{p^{\prime} = {R + 1}},\ldots \quad,{R + P + S}} )\quad ( {{t = 1},2,\ldots \quad,T} )}},( {{e = 1},2,\ldots \quad,E} )$

[0166] Next, the restriction conditions in relation with the targetvalues of the management indices will be shown.

[0167] The management indices includes the inventory, profit, sales,cost, the rate of operation, the fulfillment rate with demand amountfrom the marketing points, cash which is produced by the productionactivity, and an efficiency at which the production activity producesthe cash, and with respect to the respective indices, the target valuesthereof are combined into the restriction conditions as the constants.However, there sometimes occurs a possibility that the production plansatisfying the target values of the management indices do not exist,necessarily. In other words, there is the possibility that no regionexists, which can be executed, in the linear programming problem. Insuch the case, if giving a calculation result thereof, such as“infeasible”, it is impossible to know or acknowledge the reason why itcomes to be so. Then, according to the present invention, an actualvalue is described by the following equation:

Actual value (variable)=target value+positive estrangement from thetarget value (variable)−negative estrangement from the target value(variable)

[0168] When setting the target value for the storage at 50, for example,it comes to be as follows:

Actual value=50+positive estrangement from the target value−negativeestrangement from the target value

[0169] In a case where, as a result of solving the linear programmingproblem, there exists no solution being executable for the target value50 of the storage, then as the result thereof, the “actual value” is 40,upon the restriction condition, it comes to be 40=50+0−10, therebysatisfying the condition of “=”. By formulating in such the manner, itbecomes easy for a planner of the production plan to decide on theintention for a next action (such as, lowering the target values of themanagement indices in the relationship of trade-off, etc.).

[0170] The restriction condition of each of the management indices isshown in below.

[0171] <Restriction Condition 8: the fulfillment rate with demand amountfrom the marketing points>

[0172] Assuming that the fulfillment target value of the expectationamount of sales of the item i in the n^(th) term from the marketingpoints s be GV1, then the following is established:

[0173] (Eq. 13): Restriction Condition 8x_(it)^(s) = D_(it)^(s) + GV₁ + d_(1, s, i, t)⁺ − d_(1, s, i, t)⁻(i = 1, …  , N,  s = R + P + 1, …  , R + P + S, t = 1, 2, …  , T)d_(1, s, i, t)⁺: positive estrangement from the target valued_(1, s, i, t)⁻: negative estrangement from the target value

[0174] <Restriction Condition 9: the rate of operation>

[0175] Assuming that the target value for the rate of operation at theproduction point p be GVp2, the following is established:

[0176] (Eq. 14): Restriction Condition 9${\sum\limits_{t}{\sum\limits_{i = 1}^{N + M}\{ {K_{i}^{p} \cdot ( {R_{it}^{p} + {\sum\limits_{p^{\prime} = {R + 1}}^{R + P}W_{it}^{{pp}^{\prime}}}} )} \}}} = {{{GV}_{2}^{p} \cdot {\sum\limits_{t}C_{t}^{p}}} + d_{2,p}^{+} - {d_{2,p}^{-}( {{p = {R + 1}},\ldots \quad,{R + P}} )}}$d_(2, p)⁺: positive estrangement from the target valued_(2, p)⁻: negative estrangement from the target value

[0177] <Restriction Condition 10: the efficiency of producing cash byproduction activity>

[0178] By means of the cash which is produced by the production activityduring the period from the 1^(st) term to the T′^(th) (<T) term of aplanning term, the production plan is estimated.

[0179] A relationship between the products and the cash is shown in FIG.2. Taking the cash (money amount) on the vertical axis while the termson the horizontal axis, the term intersecting with the vertical axis isa planning term (head of one term). An arrow 201 indicates process, inwhich one (1) piece of a certain product is produced, wherein no cash isinvested for that product at the time point t when starting supply ofthe parts, however at the time point t′ passing by the time of the orderlead time+the transport lead time thereafter, the investment is made forthe unit prices of the parts+the transport cost thereof. Following withcontinuity of the production, the investment is increased, and the cost(except for the fixed cost) in relation with that product is determinedat the time point t″ when being distributed to the marketing points asthe product. Assuming that that product is sold at an instance when itreaches to the marketing point, so as to recover the cash therefor, thesales−the cost comes to be the cash which that product produces. Thisarrow is drown in a plural number during the period of the planning,therefore the cash which was invested from the planning term until theT′^(th) (<T) term is coincident with an area of a rectangular BDEH 202(restrictively speaking, it does not come to be the rectangular, sincethe cost for each of the products is not constant, but it is simplifiedfor aid of understanding thereof). Within 202, there are the investment207 (a rectangular BCEH) to be recovered until the T′^(th) (<T) term andprior investment 203 (a triangle CDE) for the purpose of selling theproduct after the T′^(th) term. The prior investment 203 will berecovered after the T′^(th) term. On the contrary, for the products withthe arrow 204, there is the cash which was invested as the priorinvestment before the planning term, and also there is one which can berecovered during the terms from the planning term to the T′^(th) term.

[0180] In such the manner, the investment in the planning term can bedivided into the investment relating to the products, from which thecash is recovered, and the prior investment for the next coming terms.It is the that the smaller on the investment, the better, and inparticular, for the product being changeable in the demand thereof amongthem, the prior investment 203 for the next coming terms, which are highon a factor of uncertainty should be better as small as possible.Therefore, obtaining more cash with a small investment comes to be themanagement index for measuring the superiority of the production plan.The obtaining of more cash with the small investment is calculatedaccording to the equation 205, as the efficiency at which the productionactivity produces the cash.

[0181] The numerator or fraction is the subtraction of the cash 202(=207+203) invested during the terms from 1^(st) to T′^(th) from thesales (206: though also the sales should not be at constant in theamount, but it is indicated by the rectangular BDFG for thesimplification, in the same manner as 202), i.e., it indicates the cash(the rectangular HEFG) obtained from the production activity during the1^(st) to T′^(th) th terms. The denominator is the addition of delayinginventory (being considered as the prior investment) to the priorinvestment 203. From this calculation, the cash per one unit of theprior investment can be calculated out. According to the presentinvention, this is defined as the efficiency of producing the cash bythe production activity.

[0182] This calculation is that applying ROA (Return On Asset) into theproduction activity.

[0183] Formulating the above calculation, the numerator comes to be thecash which is obtained through the production activity during the terms1^(st) to T′^(th), namely:

[0184] (Eq. 15): Cash obtained by production activity${\sum\limits_{i}{\sum\limits_{s}{{PR}_{i}^{s} \cdot {\sum\limits_{t = 1}^{T}x_{it}^{s}}}}} - \{ {{\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T^{\prime}}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}}}}} + {\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{i = 1}^{T^{\prime}}R_{it}^{p}}} )}} + {\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T^{\prime}}{{PO}^{p} \cdot {CO}_{t}^{p}}}}} \}$

[0185] Where the denominator comes to be the prior investment (theinventory) at the time point of the T′^(th) term, as indicated below:$ {{{ { {\text{(Eq. 16): Prior Investment (Inventory)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}{{\sum\limits_{j = 1}^{B}\{ {( {\frac{1}{R_{j}}{\sum\limits_{r \in R_{j}}{PP}_{j}^{r}}} ) \cdot \begin{Bmatrix}{{\sum\limits_{r \in R}{\sum\limits_{t = 1}^{T^{\prime}}R_{jt}^{r}}} + {\sum\limits_{r \in R}\{ {I_{j0}^{p} + {\sum\limits_{t = 1}^{T}{\sum\limits_{r = {R + 1}}^{R + P}W_{jt}^{rp}}}} \}} +} \\{{\sum\limits_{i \in M}\{ {{BMM}_{ij} \cdot ( {I_{i0} + {WIP}_{it}^{p} + W_{it}^{{pp}^{\prime}}} )} \}} -} \\{\sum\limits_{i = 1}^{N}( {{BMS}_{ij} \cdot {\sum\limits_{s}{\sum\limits_{t = 1}^{T^{\prime}}x_{it}^{s}}}} )}\end{Bmatrix}} \}} + {\sum\limits_{i = 1}^{N + M}{\sum\limits_{p \in P}{\{ {{PP}_{i}^{p} + {\sum\limits_{j = {N + 1}}^{N + M + B}( {{{BM}_{ij} \cdot \frac{1}{P_{b}}}{\sum\limits_{p^{\prime} \in P_{b}}{PM}_{j}^{p^{\prime}}}} )}} \} \cdot \{ {{I_{{iT}^{\prime}}^{p} + {\sum\limits_{t = {T^{\prime} + 1}}^{T}{\{ {R_{it}^{p}}\quad t}} - {LT}_{i}^{p}} \leq T^{\prime}} \}}}}}} \} + {\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{\underset{P^{\prime} \in {P + S}}{p \in {R + P}}}\{ {{\{ {Q_{ie}^{{pp}^{\prime}}}\quad i} \in n} \}}} + {PM}_{i}^{p}} \} \cdot {\sum\limits_{t = 1}^{T^{\prime}}{\{ {U_{iet}^{{pp}^{\prime}}}\quad t}}} + {LT}_{ie}^{{pp}^{\prime}}} > T^{\prime}} \}$

[0186] However, the first line of this equation is the product obtainedfrom multiplying the number of the parts remaining at the each point bythe unit price of part, wherein the products and/or the semi-productsare converted to the parts. Since the unit prices of parts are differentdepending upon the supply points, an average value thereof is used. Rjis a set or assembly of the supply points which can supply the part j.The second line is the product obtained from multiplying the productsand/or semi-products remaining at the production points by the sum ofthe production cost and a standard cost. The standard cost of thesemi-products (parts) j at the process p′ indicates an average valuebetween the production cost thereof, which will be necessitated frommanufacturing the semi-products (parts) j at the process p′ until theyare transported as the parts to an arbitrary process p of the productionpoints, and the transport cost. The third line is the product obtainedfrom multiplying the amount of products which are transported to eachpoint by the standard cost of products (since the transport cost to themarketing points is not included in the standard cost of products, thetransport cost is added thereto).

[0187] In case of formulating the efficiency of producing the cash bythe production activity as the restriction condition, the average valueof the prior investment, being calculated out for each of the terms, isused into the denominator, while setting the cash obtained by theproduction activity during the 1^(st) to T^(th) terms into thenumerator. This is because, if it is estimated only by the priorinvestment (the inventory) in the T′^(th) term, there is a possibilitythat the prior investment comes to be large in the terms except for thatof T′^(th), and then it is impossible to obtain a desired productionplan. Also, conducting the calculation by setting T′=T^(th) term, theproduction plan cannot be made up produced because the sales scheduleafter the T^(th) term is out of the target of the calculation, thereforethe prior investment comes to be zero (0).

[0188] From the above, the restriction condition 10 upon the efficiencyof producing the cash by the production activity comes to be as follows,assuming that the target value is GV3:(Eq. 17): Restriction condition 10                                                          ${{\sum\limits_{s}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{{PR}_{i}^{s} \cdot x_{it}^{s}}}}} - \begin{pmatrix}{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{P^{\prime} = {R + !}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}}}}} +} \\{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T}R_{it}^{p}}} )}} +} \\{\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T}{{PO}^{p} \cdot {CO}_{t}^{p}}}}\end{pmatrix}} = {{{GV}_{3} \cdot ( {\frac{1}{T}\begin{Bmatrix}{\sum\limits_{j = 1}^{B}\{ {( {\frac{1}{R_{j}}{\sum\limits_{r \in R_{j}}{PP}_{j}^{r}}} ) \cdot \{ {{\sum\limits_{r \in R}{\sum\limits_{t = 1}^{T}R_{jt}^{r}}} +} } } \\{  {\sum\limits_{r \in R}\{ {I_{j0}^{p} + {\sum\limits_{t = 1}^{T}{\sum\limits_{r = {R + 1}}^{R + P}W_{jt}^{rp}}}} \}} \} \} +} \\{{\sum\limits_{i = 1}^{N + M}{\sum\limits_{p \in P}\begin{bmatrix}{\{ {{PP}_{i}^{p} + {\sum\limits_{j = {N + 1}}^{N + M + B}( {{{BM}_{ij} \cdot \frac{1}{P_{b}}}{\sum\limits_{p \in P_{b}}{PM}_{j}^{p^{\prime}}}} )}} \} \cdot} \\\{ {\sum\limits_{t = 1}^{T}\{ {I_{it}^{p} + {R_{it}^{p} \cdot {LT}_{i}^{p}}} \}} \}\end{bmatrix}}} +} \\{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{\underset{p^{\prime} \in {P + S}}{p \in {R + P}}}{ { {{{\{ \{ {Q_{ie}^{{pp}^{\prime}}}  \quad}i} \in n} \} + {PM}_{i}^{p}} \} \cdot}}} \\{\sum\limits_{t = 1}^{T}\{ {U_{iet}^{{pp}^{\prime}} \cdot {LT}_{ie}^{{pp}^{\prime}}} \}}\end{Bmatrix}} )} + d_{3}^{+} + d_{3}^{-}}$d₃⁺: positive estrangement from the target valued₃⁻: negative estrangement from the target value

[0189] <Restriction condition 11: Sales>

[0190] Assuming that the sales target at the marketing point s is GV4,s,the following is established:

[0191] (Eq. 18): Restriction condition 11${\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{{PR}_{i}^{s} \cdot x_{it}^{s}}}} = {{GV}_{4,s} + d_{4,s}^{+} - d_{4,s}^{-}}$d_(4, s)⁺: positive estrangement from the target valued_(4, s)⁻: negative estrangement from the target value

[0192] <Restriction condition 12: Cash produced by the productionactivity>

[0193] The previous numerator of the efficiency of producing the cash bythe production activity is set to be one of the management indices. Thisindex is used when it is requested that the cash is obtained as much aspossible, regardless of the prior investment. Assuming the target valuebe GV5, the equation comes to be as follows:

[0194] (Eq. 19): Restriction condition 12${{\sum\limits_{s}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{{PR}_{i}^{5} \cdot x_{it}^{s}}}}} - \{ \begin{matrix}{\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T}{Q_{ie}^{{pp}^{\prime}} \cdot}}}}}} \\{U_{iet}^{{pp}^{\prime}} + {\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T}R_{it}^{p}}} )}} +} \\{\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T}{{PO}^{p} \cdot {CO}_{i}^{p}}}}\end{matrix} )} = {{GV}_{5} + d_{5}^{+} - d_{5}^{-}}$d₅⁺: positive estrangement from the target valued₅⁻: negative estrangement from the target value<Restriction condition 13: Profit>

[0195] Assuming that the profit target is GV6, the following isestablished:

[0196] (Eq. 20): Restriction condition 13${{\sum\limits_{s}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{{PR}_{i}^{5} \cdot x_{it}^{s}}}}} - {\sum\limits_{i = 1}^{N}{\sum\limits_{p \in P}{{PM}_{i}^{p} \cdot I_{i0}^{p}}}} - ( {\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}\begin{Bmatrix}{{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}} +} \\{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T}R_{it}^{p}}} )}} +} \\{\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{i = 1}^{N + M}{{PC}^{p} \cdot {CO}_{t}^{p}}}}\end{Bmatrix}}}} ) - {FC} + {\sum\limits_{p}{\sum\limits_{i}\{ {{PM}_{i}^{p} \cdot I_{iT}^{p}} \}}}} = {{GV}_{6} + d_{6}^{+} - d_{6}^{-}}$d₆⁺: positive estrangement from the target valued₆⁻: negative estrangement from the target value

[0197] Where the profit is, different from the cash which the productionactivity produces, the subtraction of the cost invested onto theproducts and the fixed cost from the sales, i.e., the cash which theproducts produces.

[0198] <Restriction condition 14: Cost>

[0199] Assuming that the target cost is GV7, the following equation isestablished:

[0200] (Eq. 21): Restriction condition 14${\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}}}}} + {\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T}R_{it}^{p}}} )}} + {\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T}{{PO}^{p} \cdot {CO}_{t}^{p}}}}$d₇⁺: positive estrangement from the target valued₇⁻: negative estrangement from the target value

[0201] Where the cost corresponds to the cash which is invested duringthe 1^(st) to T′^(th) terms, in the numerator of the efficiency ofproducing the cash, however it does not includes the fixed cost therein.

[0202] <Restriction condition 15: Inventory>

[0203] Assuming that the inventory target is GV8, the following equationis established: ${\frac{1}{T}\begin{Bmatrix}{{\sum\limits_{j = 1}^{B}\{ {( {\frac{1}{R_{j}}{\sum\limits_{r \in R_{j}}{PP}_{j}^{r}}} ) \cdot \{ {{\sum\limits_{r \in R}{\sum\limits_{t = 1}^{T}R_{jt}^{r}}} + {\sum\limits_{r \in R}\{ {I_{j0}^{p} + {\sum\limits_{t = 1}^{T}{\sum\limits_{r = {R + 1}}^{R + P}W_{jt}^{ro}}}} \}}} \}} \}} +} \\{\sum\limits_{i = 1}^{N + M}{\sum\limits_{p \in P}{\{ {{PP}_{i}^{p} + {\sum\limits_{j = {N + 1}}^{N + M + B}( {{{BM}_{ij} \cdot \frac{1}{P_{b}}}{\sum\limits_{p^{\prime} \in P_{b}}{PM}_{j}^{p^{\prime}}}} )}} \} \cdot}}} \\{\{ {\sum\limits_{t = 1}^{T}\{ {I_{it}^{p} + {R_{it}^{p} \cdot {LT}_{i}^{p}}} \}} \} + {\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{\underset{p^{\prime} \in {P + S}}{p \in {R + P}}}{ { {{{\{ \{ {Q_{ie}^{{pp}^{\prime}}}  \quad}i} \in n} \} + {PM}_{i}^{p}} \} \cdot}}}} \\{\sum\limits_{t = 1}^{T}\{ {U_{iet}^{{pp}^{\prime}} \cdot {LT}_{ie}^{{pp}^{\prime}}} \}}\end{Bmatrix}} = {{GV}_{8} + d_{8}^{+} + d_{8}^{-}}$d₈⁺: positive estrangement from the target valued₈⁻: negative estrangement from the target value

[0204] Where the inventory corresponds to the denominator of theefficiency of producing the cash.

[0205] The restriction conditions 8 to 15 of the above-mentionedmanagement indices are taken into the linear programming problem onlywhen management targets are set.

[0206] According to the present invention, when setting the target, withrespect to the concrete target value, it is selected whether an actualnumerical value is desired to be equal or greater or less than that, orcoincident with that. Alternatively, it may be not such the targetvalue, but may be set as “maximum” or “minimum”. Hereinafter, thosechoices are called by a name of flag. In addition to the flag, weight isgiven on the management index or indices, which are considered to beimportant.

[0207] Assuming that all the management targets are set, then theobjective function comes to be as follows:(Eq. 23): Objective functions                                                                       ${\min \quad {F_{1}^{-} \cdot {\sum\limits_{s = 1}^{S}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{Z_{1} \cdot {PR}_{i}^{s} \cdot d_{1,s,i,t}^{-}}}}}}} + {F_{1}^{+} \cdot {\sum\limits_{s = 1}^{S}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{Z_{1,s,i} \cdot {PR}_{i}^{s} \cdot d_{1,s,i,t}^{+}}}}}} + {F_{2}^{-} \cdot {\sum\limits_{p = 1}^{P}{Z_{2,p} \cdot d_{2,p}^{-}}}} + {F_{2}^{+} \cdot {\sum\limits_{p = 1}^{P}{Z_{,{p2}} \cdot d_{2,p}^{+}}}} + {F_{3}^{-} \cdot Z_{3} \cdot d_{3}^{-}} + {F_{2}^{+} \cdot Z_{3} \cdot d_{3}^{+}} + {F_{4}^{-} \cdot Z_{4,s} \cdot d_{4,s}^{-}} + {F_{4}^{+} \cdot Z_{4,s} \cdot d_{4,s}^{+}} + {F_{5}^{-} \cdot Z_{5} \cdot d_{5,p}^{-}} + {F_{5}^{+} \cdot Z_{5} \cdot d_{5,p}^{+}} + {F_{6}^{-} \cdot Z_{6} \cdot d_{6}^{-}} + {F_{6}^{+} \cdot Z_{6} \cdot d_{6}^{+}} + {F_{7}^{-} \cdot Z_{7} \cdot d_{7}^{-}} + {F_{7}^{+} \cdot Z_{7} \cdot d_{7}^{+}} + {F_{8}^{-} \cdot Z_{8} \cdot d_{8}^{-}} + {F_{8}^{+} \cdot Z_{8} \cdot d_{8}^{+}}$

[0208] Where F. is the flag, and regarding F+, it is:

[0209] equal or greater than the target value: −1

[0210] equal or less than the target value: 1

[0211] coincident with: 1

[0212] maximum: −A (A: for some positive number)

[0213] minimum: A,

[0214] and regarding F−, it is:

[0215] equal or greater than the target value: 1

[0216] equal or less than the target value: −1

[0217] coincident with: 1

[0218] maximum: A (A: for some positive number)

[0219] minimum: −A.

[0220] Also, Z. indicates the weighting on each of the managementindices.

[0221] Next, according to the modeling indicated by those equations,Eqs. 1 to 23, the flows up to planning of the production plan will beshown in FIG. 3.

[0222] In a step 301 are inputted the data of the constantscorresponding to the Eq. 2 and the target values of the managementindices. The data relating to the target values of the management indexare made of the “management index”, a “mark for determining whetherbeing set or not”, the “flag”, and the “target value”.

[0223] In a step 302, non-negative conditions of the Eq.3 and the linearprogramming equations indicated in the Eqs. 4 to 22 are solved. Eachitem of the restriction conditions 8 to 15 relating to the managementindices and the objective functions is selected to be relevant with the“being set” management index, by referring to the “mark for determiningwhether being set or not” thereof, so as to be added to the linearprogramming problems. Also, with respect to the restriction conditions 1to 7, the restriction condition 3 may deleted if it is desired to deletethe restriction upon the production capacity, while the restrictioncondition 7 may be deleted if it is desired to delete the restrictionupon the transportation capacity.

[0224] As a means for solving the linear programming problems may beapplied a linear programming software package, or a simplex method, oran interior point method, etc.

[0225] In a step 303, optimal solutions obtained in 302 are converted tothe production plan, and are displayed on a display means, such as aCRT, etc. According to the present invention, the following variablesform the production plan:

[0226] (Eq. 24) Production Plan

[0227] R_(it) ^(p): amount of the part i to be newly supplied from thesupply point p in the t^(th) term (material supply plan) however,

[0228] (i=N+M+1, . . . , N+M+B),

[0229] (t=1,2, . . . , T)

[0230] (p=1,2, . . . , R);

[0231] R_(it) ^(p): amount of the semi-product or the product i producedat the production point p in the t^(th) term (products/semi-productsproduction plan) however,

[0232] (i=1, . . . , N+M),

[0233] (t=1,2, . . . , T)

[0234] (p=R+1, . . . , R+P);

[0235] X_(it) ^(s): amount of product i to be delivered to the marketingpoint s in the t^(th) term (sales plan)

[0236] (s=(p=)R+P+1,R+P+2, . . . , R+P+S)

[0237] (i=1,2, . . . , N)

[0238] (t=1, 2, . . . , T);

[0239] U_(iet) ^(pp′): amount of the part i to be transported from theprocess p to p′ by means e in the t^(th) term (transportation plan)

[0240] (I=N+1,N+2, . . . , N+M+B),

[0241] (t=1,2, . . . , T),

[0242] (p=1,2, . . . , R+P+S); and

[0243] Co_(t) ^(p): the over time at the process p in the t^(th) term(capacity plan)

[0244] Also, from the optimal solutions obtained in 302, “actual values”of all the management indices are calculated to be displayed on thedisplay means, such as the CRT, etc. The “actual values” of all themanagement indices are calculated by the following equations:(Eq. 25) Equation for calculating out the management indices:             the fulfillment of demands from the marketing points$\frac{x_{it}^{s}}{D_{it}^{s}},( {{i = 1},\ldots \quad,N,{s = {R + P + 1}},\ldots \quad,{R + P + S},{t = 1},\ldots \quad,T} )$(Eq. 26) Equation for calculating out the management indices:              the rate of operation$\frac{\sum\limits_{t}{\sum\limits_{i = 1}^{N + M}\{ {K_{i}^{p} \cdot ( {R_{it}^{p} + {\sum\limits_{p^{\prime} = {R + 1}}^{R + P}W_{it}^{{pp}^{\prime}}}} )} \}}}{\sum\limits_{t}C_{t}^{p}},( {{p = {R + 1}},\ldots \quad,{R + P}} )$

[0245] (Eq. 27) Equation for calculating out the management indices: theefficiency of producing the cash by the production activity$\frac{\begin{matrix}{{\sum\limits_{i}{\sum\limits_{s}{{PR}_{i}^{s\quad} \cdot {\sum\limits_{t = 1}^{T^{\prime}}x_{it}^{s}}}}} -} \\\begin{Bmatrix}{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T^{\prime}}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}}}}} +} \\{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T^{\prime}}R_{it}^{p}}} )}} +} \\{\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T^{\prime}}{{PO}^{p} \cdot {CO}_{t}^{p}}}}\end{Bmatrix}\end{matrix}}{\begin{matrix}{{\sum\limits_{j = 1}^{B}\begin{Bmatrix}{( {\frac{1}{R_{j}}{\sum\limits_{r \in R_{j}}{PP}_{j}^{r}}} ) \cdot} \\\begin{Bmatrix}{{\sum\limits_{r \in R}{\sum\limits_{t = 1}^{T^{\prime}}R_{jt}}} + {\sum\limits_{r \in R}\{ {I_{j0}^{p} + {\sum\limits_{t = 1}^{T}{\sum\limits_{r = {R + 1}}^{R + P}W_{jt}^{rp}}}} \}} +} \\{{\sum\limits_{i \in M}\{ {{BMM}_{ij} \cdot ( {I_{i0} + {WIP}_{it}^{p} + W_{it}^{{pp}^{\prime}}} )} \}} -} \\{\sum\limits_{i = 1}^{N}( {{BMS}_{ij} \cdot {\sum\limits_{s}{\sum\limits_{t = 1}^{T^{\prime}}x_{it}^{s}}}} )}\end{Bmatrix}\end{Bmatrix}} +} \\{{\sum\limits_{i = 1}^{N + M}{\sum\limits_{p \in P}\begin{bmatrix}{\{ {{PP}_{i}^{p} + {\sum\limits_{j = {N + 1}}^{N + M + B}( {{{BM}_{ij} \cdot \frac{1}{P_{b}}}{\sum\limits_{p^{\prime} \in P_{b}}{PM}_{j}^{p^{\prime}}}} )}} \} \cdot} \\  {{{{\{ {I_{{iT}^{\prime}}^{p} + {\sum\limits_{t = {T^{\prime} + 1}}^{T}\{ {R_{it}^{p}} }} \quad}t} - {LT}_{i}^{p}} \leq T^{\prime}} \} \}\end{bmatrix}}} +} \\{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{\underset{p^{\prime} \in {P + S}}{p \in {R + P}}}\begin{Bmatrix}{ {{{\{ {Q_{ie}^{{pp}^{\prime}}} \quad}i} \in n} \} + {{PM}_{i}^{p} \cdot}} \\ {\sum\{ {U_{iet}^{{pp}^{\prime}}{{{t + {LT}_{ie}^{{pp}^{\prime}}} > T^{\prime}}}} } \}\end{Bmatrix}}}\end{matrix}}$

$\begin{matrix}\text{(Eq. 28) Equation for calculating out the management indices:the sales} \\{{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T}{{PR}_{i}^{s} \cdot x_{it}^{s}}}},\quad ( {{s = {R + P + 1}},\ldots \quad,{R + P + S}} )}\end{matrix}$

[0246] (Eq. 29) Equation for calculating out the management indices: thecash which the production activity produces${\sum\limits_{s}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T^{\prime}}{{PR}_{i}^{s} \cdot x_{it}^{s}}}}} - \begin{pmatrix}{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T^{\prime}}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}}}}} +} \\{{\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T^{\prime}}R_{it}^{p}}} )}} +} \\{\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T^{\prime}}{{PO}^{p} \cdot {CO}_{t}^{p}}}}\end{pmatrix}$

[0247] (Eq. 30) Equation for calculating out the management indices: theprofit${\sum\limits_{s}{\sum\limits_{i = 1}^{N}{\sum\limits_{t = 1}^{T^{\prime}}{{PR}_{i}^{s} \cdot x_{it}^{s}}}}} - {\sum\limits_{i = 1}^{N}{\sum\limits_{p \in P}{{PM}_{i}^{p} \cdot I_{i0}^{p}}}} - ( {\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}\begin{bmatrix}{{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T^{\prime}}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}} + {\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T^{\prime}}R_{it}^{p}}} )}} +} \\{\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{i = 1}^{N + M}{{PO}^{p} \cdot {CO}_{t}^{p}}}}\end{bmatrix}}}} ) - {FC}$

[0248] (Eq. 31) Equation for calculating out the management indices: thecost${\sum\limits_{p = 1}^{R + P}{\sum\limits_{p^{\prime} = {R + 1}}^{R + P + S}{\sum\limits_{i = 1}^{N + M + B}{\sum\limits_{e = 1}^{E}{\sum\limits_{t = 1}^{T^{\prime}}{Q_{ie}^{{pp}^{\prime}} \cdot U_{iet}^{{pp}^{\prime}}}}}}}} + {\sum\limits_{p = 1}^{R + P}{\sum\limits_{i = 1}^{N + M + B}( {{PP}_{i}^{p} \cdot {\sum\limits_{t = 1}^{T^{\prime}}R_{it}^{p}}} )}} + {\sum\limits_{p = {R + 1}}^{R + P}{\sum\limits_{t = 1}^{T^{\prime}}{{PO}^{p} \cdot {CO}_{t}^{p}}}}$

(Eq. 32) Equation for calculating out the management indices:the inventory${\sum\limits_{j = 1}^{B}\{ {( {\frac{1}{R}{\sum\limits_{r \in R}{PP}_{j}^{r}}} ) \cdot \{ {{\sum\limits_{r \in R}{\sum\limits_{t = 1}^{T}R_{jt}^{r}}} + {\sum\limits_{r \in R}\{ {I_{j0}^{p} + {\sum\limits_{t = 1}^{T}{\sum\limits_{r = {R + 1}}^{R + P}W_{jt}^{rp}}}} \}} - {\sum\limits_{i = 1}^{N}( {{BMS}_{ij} \cdot {\sum\limits_{s}{\sum\limits_{t = 1}^{T^{\prime}}x_{it}^{s}}}} )}} \}} \}} + {\sum\limits_{i = 1}^{N + M}{\sum\limits_{p \in P}{\{ {{PP}_{i}^{p} + {\sum\limits_{j = {N + 1}}^{N + M + B}( {{BM}_{ij} \cdot {PM}_{j}^{p}} )}} \} \cdot \{ {I_{{iT}^{\prime}}^{p} + {\sum\limits_{t = {T^{\prime} + 1}}^{T}\{ {R_{it}^{p} {{t - {LT}_{i}^{p}} \leq T^{\prime}} \}} \}} + {\sum\limits_{i = 1}^{N}{\sum\limits_{p \in P}{\{ {Q_{ie}^{ps} + {PM}_{i}^{p}} \} \cdot {\sum\limits_{t = 1}^{T^{\prime}}\{ {{{U_{iet}^{ps}{\quad}t} + {LT}_{ie}^{ps}} > T^{\prime}} \}}}}}} }}}$

[0249] It does not matter that the production plan and/or the managementindices is/are displayed in the form of a table (or chart) or a graph.

[0250] The person in charge of the production plan confirms theproduction plan and the management indices from the display means, suchas the CRT, so as to decide to be satisfied with that production plan ornot. If it is not good, in a step 304, the target values of themanagement indices are changed though an input means, such as akeyboard, and the flow is turned back to the processes after the step302.

[0251] In this manner, though the steps 302 to 304 are executedrepetitively until the satisfactory production plan is calculated out,by displaying the production plan and the management indices in the step303, it is possible to estimate the merits of the production plan inview of the management indices, and further, even in a case there arethe management indices being in a trade-off relationship between them,by setting the lowest values to be satisfied, being desirous for theperson in charge of that production plan, as the respective targetvalues of the management indices, the solution is obtained by takingthose target values into the consideration, therefore it is possible toobtain the satisfactory production plan soon.

[0252] Regarding the steps 301 to 304 mentioned above, the processeswill be explained in more details thereof, with referring to an exampleof the production plan of the product “PC”.

[0253] In FIG. 4 are shown the bill of materials of the “PC”. One (1)unit of the product “PC” is produced by using one (1) unit of ansemi-product “HDD” and two (2) units of parts “CPUs”. Also, the one (1)unit of semi-product “HDD” is produced by using one (1) unit of a part“DISK”. With the points, as shown in FIG. 5, the marketing points of PCare three (3), M1, M2, and M3, the production points of PC are two (2),P1 and P2, the production point of HDD is one (1), P3, and a supplypoint of CPU and DISK is one (1), V1. In FIG. 6 is shown a transportableroute and/or a transport lead time/cost per a transport means betweenthe points. The transport route and the transport means from the supplypoint to the production point and between the production points are onlyone way each, however there are two (2) means as the transport meansfrom the production points P1 and P2 to the marketing points M1, M2 andM3 at the maximum. One of them is transport via an airplane, and theother is that via a ship, and the transport of the airplane is shorterthan that of the ship in the lead-time, however is high in the transportcost. There is no specific restriction upon the capacity oftransportation. Also, the fixed cost at the points as a whole is ten(10).

[0254] Under such the basis, assuming the case where the expectationamount of sales of PC from each marketing point is 100 in the 10^(th)term during the planning terms from the 1^(st) term to 10^(th) term, theproduction plan for each of the production points is planned. Theselling price of the PC is assumed to be 45 at M1, 30 at M2, and 35 atM3, respectively. It is assumed that the operable time in each of theproduction points M1 and M2 is 70 for every term, the operable time ofM3 is 300 for every term, and no over time is possible in each of thepoints. The operation times, the lead times, and the costs of the PC andthe HDD, at each of the points, are as shown in FIG. 7. Also, theoperation time, the lead time, the unit price and the standard cost atthe supply point V1 of the CPU and DISK are as shown in FIG. 8. Theinventory at the end of the 0^(th) term and the released order and/orwork in process in a warehouse are assumed to be zero (0). Since thereis only one way in the flow of goods from the parts to thesemi-products, points in determination of intention in this example arethe production points of the PC, the transportation route from theproduction points to the marketing points, and the transportation means.

[0255] First, upon the basis of the concrete example described above,the restriction conditions 1 to 6 are formulated as below. However, therestriction condition 7 is not necessary since there is no limitation inthe transportation capacity.

[0256] <Restriction condition 1>

[0257] (Eq. 33) Restriction condition 1 in the exerciseI_(PC, t)^(P1) = I_(PC, t − 1)^(P1) + R_(PC, t)^(P1) − U_(PC, Car, t)^(P1, M1) − U_(PC, Airplane, t)^(P1, M2) − U_(PC, Ship, t)^(P1, M2) − U_(PC, Airplane, t)^(P1, M3) − U_(PC, Ship, t)^(P1, M3)I_(PC, t)^(P2) = I_(PC, t − 1)^(P2) + R_(PC, t)^(P2) − U_(PC, Airplane, t)^(P2, M1) − U_(PC, Ship, t)^(P2, M1) − U_(PC, Airplane, t)^(P2, M2) − U_(PC, Ship, t)^(P2, M2) − U_(PC, Car, t)^(P2, M3)I_(HDD, t)^(P3) = I_(HDD, t − 1)^(P3) + R_(HDD, t)^(P3) − U_(HDD, Car, t)^(P3, P1) − U_(HDD, Car, t)^(P3, P2)I_(CPU, t)^(V1) = I_(CPu, t − 1)^(V1) + R_(CPU, t)^(V1) − U_(CPU, Car, t)^(V1, P1) − U_(CPU, Car, t)^(V1, P2)I_(DISK, t)^(V1) = I_(DISK, t − 1)^(V1) + R_(DISK, t)^(V1) − U_(DISK, Car, t)^(V1, P3)(t = 1, 2, …  , T)

[0258] <Restriction condition 2>

[0259] (Eq. 34) Restriction condition 2 in the exercise{U_(CPU, Car, t − 1)^(V1, P1)t − 1 ≥ 1} = {2 ⋅ R_(PC, t + 1)^(P1)t + 1 ≤ T}{U_(CPU, Car, t − 1)^(V1, P2)t − 1 ≥ 1} = {2 ⋅ R_(PC, t + 2)^(P2)t + 2 ≤ T}{U_(DISK, Car, t − 1)^(V1, P3)t − 1 ≥ 1} = {R_(HDD, t + 1)^(P3)t + 1 ≤ T}{U_(HDD, Car, t − 1)^(V3, P1)t − 1 ≥ 1} = {R_(PC, t + 1)^(P1)t + 1 ≤ T}{U_(HDD, Car, t − 1)^(V3, P2)t − 1 ≥ 1} = {R_(PC, t + 2)^(P2)t + 2 ≤ T}(t = 1, 2, …  , T)

[0260] <Restriction condition 3>

[0261] (Eq. 35) Restriction condition 3 in the exercise1 ⋅ R_(PC, t)^(P1) ≤ 70 1 ⋅ R_(PC, t)^(P2) ≤ 701 ⋅ R_(HDD, t)^(P3) ≤ 300 (t = 1, 2, …  , T)

[0262] <Restriction condition 4>

[0263] (Eq. 36) Restriction condition 4 in the exerciseR_(CPU, 1)^(V1) = 0 R_(DISK, 1)^(V1) = 0 R_(HDD, 1)^(V3) = 0R_(CPU, 1)^(P1) = 0 R_(CPU, 1)^(P2) = 0 R_(CPU, 2)^(P2) = 0

[0264] <Restriction condition 5>

[0265] (Eq. 37) Restriction condition 5 in the exerciseU_(PC, Car, t − 1)^(P1, M1) + U_(PC, Airplane, t − 2)^(P2, M1) + U_(PC, Ship, t − 3)^(P2, M1) = x_(PC, t)^(M1)U_(PC, Airplane, t − 2)^(P1, M2) + U_(PC, Ship, t − 3)^(P1, M2) + U_(PC, Airplane, t − 2)^(P2, M2) + U_(PC, Ship, t − 3)^(P2, M2) = x_(PC, t)^(M2)U_(PC, Airplane, t − 2)^(P1, M3) + U_(PC, Ship, t − 3)^(P1, M3) + U_(PC, Car, t − 1)^(P2, M3) = x_(PC, t)^(M3)(t = 1, 2, …  , T)

[0266] <Restriction condition 6>

[0267] (Eq. 38) Restriction condition 6 in the exercise0 ≥ x_(PC, t)^(M1), (t = 1, …  , 9)0 ≥ x_(PC, t)^(M2), (t = 1, …  , 9)0 ≥ x_(PC, t)^(M3), (t = 1, …  , 9) 100 ≥ x_(PC, 10)^(M1)100 ≥ x_(PC, 10)^(M2) 100 ≥ x_(PC, 10)^(M3)

[0268] The restriction conditions 8 to 15 relating to the target valuesof the management indices are formulated as follows:

[0269] <Restriction condition 8>

[0270] (Eq. 39) Restriction condition 8 in the exercisex_(PC, t)^(M1) = 0 ⋅ GV₁ + d_(1, M1, PC, t)⁺ − d_(1, M1, PC, t)⁻, (t = 1, …  , 9)x_(PC, t)^(M2) = 0 ⋅ GV₁ + d_(1, M1, PC, t)⁺ − d_(1, M1, PC, t)⁻, (t = 1, …  , 9)x_(PC, t)^(M3) = 0 ⋅ GV₁ + d_(1, M1, PC, t)⁺ − d_(1, M1, PC, t)⁻, (t = 1, …  , 9)x_(PC, 10)^(M1) = 100 ⋅ GV₁ + d_(1, M1, PC, 10)⁺ − d_(1, M1, PC, 10)⁻x_(PC, 10)^(M2) = 100 ⋅ GV₁ + d_(1, M1, PC, 10)⁺ − d_(1, M1, PC, 10)⁻x_(PC, 10)^(M3) = 100 ⋅ GV₁ + d_(1, M1, PC, 10)⁺ − d_(1, M1, PC, 10)⁻

[0271] <Restriction condition 9>

[0272] (Eq. 40) Restriction condition 9 in the exercise1 ⋅ R_(PC, t)^(P1) = GV₂^(p) ⋅ 70 + d_(2, P)⁺ − d_(2, p)⁻1 ⋅ R_(PC, t)^(P2) = GV₂^(p) ⋅ 70 + d_(2, P)⁺ − d_(2, p)⁻1 ⋅ R_(HDD, t)^(P3) = GV₂^(p) ⋅ 300 + d_(2, P)⁺ − d_(2, p)⁻

[0273] <Restriction condition 10>

[0274] (Eq. 41) Restriction condition 10 in the exercise${{\sum\limits_{t = 1}^{T}\{ {{45 \cdot x_{{PC},t}^{M1}} + {30 \cdot x_{{PC},t}^{M2}} + {35 \cdot x_{{PC},t}^{M3}}} \}} - \begin{pmatrix}{{\sum\limits_{t = 1}^{T}\{ \begin{matrix}{{6 \cdot U_{{PC},{Car},t}^{{P1},{M1}}} + {10 \cdot U_{{PC},{Airplane},t}^{{P1},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P1},{M2}}} +} \\{{10 \cdot U_{{PC},{Airplane},t}^{{P1},{M3}}} + {7 \cdot U_{{PC},{Ship},t}^{{P1},{M3}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M1}}} +} \\{{7 \cdot U_{{PC},{Ship},t}^{{P2},{M1}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P2},{M2}}} +} \\{{4 \cdot U_{{PC},{Car},t}^{{P2},{M3}}} + U_{{HDD},{Car},t}^{{P3},{P1}} + U_{{HDD},{Car},t}^{{P3},{P2}} +} \\{U_{{CPU},{Car},t}^{{V1},{P1}} + U_{{CPU},{Car},t}^{{V1},{P2}} + U_{{DISK},{Car},t}^{{V1},{P3}}}\end{matrix}\quad \}} +} \\{\sum\limits_{t = 1}^{T}\{ {R_{{PC},t}^{P1} + {3 \cdot R_{{PC},t}^{P2}} + R_{{HDD},t}^{P3} + {5 \cdot R_{{CPU},t}^{V1}} + {3 \cdot R_{{DISK},t}^{V1}}} \}}\end{pmatrix}} = {{{GV}_{3} \cdot ( {\frac{1}{T}\begin{Bmatrix}{{\sum\limits_{t = 1}^{T}\{ {{5 \cdot R_{{CPU},t}^{V1}} + {3 \cdot R_{{DISK},t}^{V1}}} \}} +} \\{{\sum\limits_{t = 1}^{T}\begin{Bmatrix}{{( {1 + 5} )R_{{PC},t}^{P1}} + {( {2 + 5} )R_{{PC},t}^{P2}} +} \\{( {1 + 1} )R_{{HDD},t}^{P3}}\end{Bmatrix}} +} \\{\sum\limits_{t = 1}^{T}\begin{Bmatrix}{{( {6 + 7} ) \cdot U_{{PC},{Car},t}^{{P1},{M1}}} + {( {10 + 7} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P2},{M2}} + {( {8 + 7} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P1},{M2}} + {( {10 + 7} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P1},{M3}} + {( {7 + 7} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P1},{M3}} + {( {9 + 5} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P2},{M1}} + {( {7 + 5} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P2},{M1}} + {( {9 + 5} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P2},{M2}} + {( {8 + 5} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P2},{M2}} + {( {4 + 5} ) \cdot}} \\{U_{{PC},{Car},t}^{{P2},{M3}} + {3 \cdot U_{{HDD},{Car},t}^{{P3},{P1}}} + {3 \cdot}} \\{U_{{HDD},{Car},t}^{{P3},{P2}} + U_{{CPU},{Car},t}^{{V1},{P1}} +} \\{U_{{CPU},{Car},t}^{{V1},{P2}} + U_{{DISK},{Car},t}^{{V1},{P3}}}\end{Bmatrix}}\end{Bmatrix}} )} + d_{3}^{+} - d_{3}^{-}}$

[0275] <Restriction condition 11>

[0276] (Eq. 42) Restriction condition 11 in the exercise${\sum\limits_{t = 1}^{T}\{ {45 \cdot x_{{PC},t}^{M1}} \}} = {{GV}_{4,{M1}} + d_{4,{M1}}^{+} - d_{4,{M1}}^{-}}$${\sum\limits_{t = 1}^{T}\{ {30 \cdot x_{{PC},t}^{M2}} \}} = {{GV}_{4,{M2}} + d_{4,{M2}}^{+} - d_{4,{M2}}^{-}}$${\sum\limits_{t = 1}^{T}\{ {35 \cdot x_{{PC},t}^{M3}} \}} = {{GV}_{4,{M3}} + d_{4,{M3}}^{+} - d_{4,{M3}}^{-}}$

[0277] <Restriction condition 12>

[0278] (Eq. 43) Restriction condition 12 in the exercise${{\sum\limits_{t = 1}^{T}\{ {{45 \cdot x_{{PC},t}^{M1}} + {30 \cdot x_{{PC},t}^{M2}} + {35 \cdot x_{{PC},t}^{M3}}} \}} - \begin{pmatrix}{{\sum\limits_{t = 1}^{T}\begin{Bmatrix}{{6 \cdot U_{{PC},{Car},t}^{{P1},{M1}}} + {10 \cdot U_{{PC},{Airplane},t}^{{P1},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P1},{M2}}} +} \\{{10 \cdot U_{{PC},{Airplane},t}^{{P1},{M3}}} + {7 \cdot U_{{PC},{Ship},t}^{{P1},{M3}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M1}}} +} \\{{7 \cdot U_{{PC},{Ship},t}^{{P2},{M1}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P2},{M2}}} +} \\{{4 \cdot U_{{PC},{Car},t}^{{P2},{M3}}} + U_{{HDD},{Car},t}^{{P3},{P1}} + U_{{HDD},{Car},t}^{{P3},{P2}} +} \\{{{U_{{CPU},{Car},t}^{{V1},{P1}}U_{{CPU},{Car},t}^{{V1},{P2}}} + U_{{DISK},{Car},t}^{{V1},{P3}}}\quad}\end{Bmatrix}} +} \\{\sum\limits_{t = 1}^{T}\{ {R_{{PC},t}^{P1} + {3 \cdot R_{{PC},t}^{P2}} + R_{{HDD},t}^{P3} + {5 \cdot R_{{CPU},t}^{V1}} + {3 \cdot R_{{DISK},t}^{V1}}} \}}\end{pmatrix}} = {{GV}_{5} + d_{5}^{+} - d_{5}^{-}}$

[0279] <Restriction condition 13>

[0280] (Eq. 44) Restriction condition 13 in the exercise${{\sum\limits_{t = 1}^{T}\{ {{45 \cdot x_{{PC},t}^{M1}} + {30 \cdot x_{{PC},t}^{M2}} + {35 \cdot x_{{PC},t}^{M3}}} \}} - \begin{pmatrix}{{\sum\limits_{t = 1}^{T}\begin{Bmatrix}{{6 \cdot U_{{PC},{Car},t}^{{P1},{M1}}} + {10 \cdot U_{{PC},{Airplane},t}^{{P1},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P1},{M2}}} +} \\{{10 \cdot U_{{PC},{Airplane},t}^{{P1},{M3}}} + {7 \cdot U_{{PC},{Ship},t}^{{P1},{M3}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M1}}} +} \\{{7 \cdot U_{{PC},{Ship},t}^{{P2},{M1}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P2},{M2}}} +} \\{{4 \cdot U_{{PC},{Car},t}^{{P2},{M3}}} + U_{{HDD},{Car},t}^{{P3},{P1}} + U_{{HDD},{Car},t}^{{P3},{P2}} +} \\{{{U_{{CPU},{Car},t}^{{V1},{P1}}U_{{CPU},{Car},t}^{{V1},{P2}}} + U_{{DISK},{Car},t}^{{V1},{P3}}}\quad}\end{Bmatrix}} +} \\{\sum\limits_{t = 1}^{T}\{ {R_{{PC},t}^{P1} + {3 \cdot R_{{PC},t}^{P2}} + R_{{HDD},t}^{P3} + {5 \cdot R_{{CPU},t}^{V1}} + {3 \cdot R_{{DISK},t}^{V1}}} \}}\end{pmatrix} - 10 + {7 \cdot I_{{PC},T}^{P1}} + {5 \cdot I_{{PC},T}^{P2}} + {3 \cdot I_{{HDD},T}^{P3}} + I_{{CPU},T}^{V1} + I_{{DISK},T}^{V1}} = {{GV}_{6} + d_{6}^{+} - d_{6}^{-}}$

[0281] <Restriction condition 14>

[0282] (Eq. 45) Restriction condition 14 in the exercise${{\sum\limits_{t = 1}^{T}\begin{Bmatrix}{{6 \cdot U_{{PC},{Car},t}^{{P1},{M1}}} + {10 \cdot U_{{PC},{Airplane},t}^{{P1},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P1},{M2}}} +} \\{{10 \cdot U_{{PC},{Airplane},t}^{{P1},{M3}}} + {7 \cdot U_{{PC},{Ship},t}^{{P1},{M3}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M1}}} +} \\{{7 \cdot U_{{PC},{Ship},t}^{{P2},{M1}}} + {9 \cdot U_{{PC},{Airplane},t}^{{P2},{M2}}} + {8 \cdot U_{{PC},{Ship},t}^{{P2},{M2}}} +} \\{{4 \cdot U_{{PC},{Car},t}^{{P2},{M3}}} + U_{{HDD},{Car},t}^{{P3},{P1}} + U_{{HDD},{Car},t}^{{P3},{P2}} +} \\{{{U_{{CPU},{Car},t}^{{V1},{P1}}U_{{CPU},{Car},t}^{{V1},{P2}}} + U_{{DISK},{Car},t}^{{V1},{P3}}}\quad}\end{Bmatrix}} + {\sum\limits_{t = 1}^{T}\{ {R_{{PC},t}^{P1} + {3 \cdot R_{{PC},t}^{P2}} + R_{{HDD},t}^{P3} + {5 \cdot R_{{CPU},t}^{V1}} + {3 \cdot R_{{DISK},t}^{V1}}} \}}} = {{GV}_{7} + d_{7}^{+} - d_{7}^{-}}$

[0283] <Restriction condition 15>

[0284] (Eq. 46) Restriction condition 15 in the exercise${\frac{1}{T}\begin{Bmatrix}{{\sum\limits_{t = 1}^{T}\{ {{5 \cdot R_{{CPU},t}^{V1}} + {3 \cdot R_{{DISK},t}^{V1}}} \}} + {\sum\limits_{t = 1}^{T}\{ {{( {1 + 5} )R_{{PC},t}^{P1}} +} }} \\{ {{( {2 + 5} )R_{{PC},t}^{P2}} + {( {1 + 1} )R_{{HDD},t}^{P3}}} \} +} \\{\sum\limits_{t = 1}^{T}\begin{Bmatrix}{{( {6 + 7} ) \cdot U_{{PC},{Car},t}^{{P1},{M1}}} + {( {10 + 7} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P1},{M2}} + {( {8 + 7} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P1},{M2}} + {( {10 + 7} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P1},{M3}} + {( {7 + 7} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P1},{M3}} + {( {9 + 5} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P2},{M1}} + {( {7 + 5} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P2},{M1}} + {( {9 + 5} ) \cdot 2 \cdot}} \\{U_{{PC},{Airplane},t}^{{P2},{M2}} + {( {8 + 5} ) \cdot 3 \cdot}} \\{U_{{PC},{Ship},t}^{{P2},{M2}} + {( {4 + 5} ) \cdot}} \\{U_{{PC},{Car},t}^{{P2},{M3}} + {3 \cdot}} \\{U_{{HDD},{Car},t}^{{P3},{M1}} + {3 \cdot U_{{HDD},{Car},t}^{{P3},{P2}}} +} \\{U_{{CPU},{Car},t}^{{V1},{P1}} + U_{{CPU},{Car},t}^{{V1},{P2}} +} \\U_{{DISK},{Car},t}^{{V1},{P3}}\end{Bmatrix}}\end{Bmatrix}} = {{GV}_{8} + d_{8}^{+} - d_{8}^{-}}$

[0285] The objective function is as follows:

[0286] (Eq. 47) Objective function in the exercise${\min \quad {F_{1}^{-} \cdot Z_{1}}\{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{-}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{-}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{-}}}} \}} + {{F_{1}^{+} \cdot Z_{1}}\{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{+}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{+}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{+}}}} \}} + {F_{2}^{-}\{ {{Z_{2,{P1}} \cdot d_{2,{P1}}^{-}} + {Z_{2,{P2}} \cdot d_{2,{P2}}^{-}} + {Z_{2,{P3}} \cdot d_{2,{P3}}^{-}}} \}} + {F_{2}^{+}\{ {{Z_{2,{P1}} \cdot d_{2,{P1}}^{+}} + {Z_{2,{P2}} \cdot d_{2,{P2}}^{+}} + {Z_{2,{P3}} \cdot d_{2,{P3}}^{+}}} \}} + {F_{3}^{-} \cdot Z_{3} \cdot d_{3}^{-}} + {F_{2}^{+} \cdot Z_{3} \cdot d_{3}^{+}} + {F_{4}^{-} \cdot Z_{4,s} \cdot d_{4,s}^{-}} + {F_{4}^{+} \cdot Z_{4,s} \cdot d_{4,s}^{+}} + {F_{5}^{-} \cdot Z_{5} \cdot d_{5,p}^{-}} + {F_{5}^{+} \cdot Z_{5} \cdot d_{5,p}^{+}} + {F_{6}^{-} \cdot Z_{6} \cdot d_{6}^{-}} + {F_{6}^{+} \cdot Z_{6} \cdot d_{6}^{+}} + {F_{7}^{-} \cdot Z_{7} \cdot d_{7}^{-}} + {F_{7}^{+} \cdot Z_{7} \cdot d_{7}^{+}} + {F_{8}^{-} \cdot Z_{8} \cdot d_{8}^{-}} + {F_{8}^{+} \cdot Z_{8} \cdot d_{8}^{+}}$

[0287] As a first example (exercise 1) of the panning of a productionplan, the production plan is planned only by the management index, i.e.,the fulfillment of demands from the marketing points is 100%. Therestriction condition is, in addition to those 1 to 6, GV1=1, forexample, in the restriction condition 8. Those from 9 to 15 are notused. The objective functions are as follows:

[0288] (Eq. 48) Objective function in the exercise 1${\min \quad \{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{-}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{-}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{-}}}} \}} + \{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{+}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{+}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{+}}}} \}$

[0289] When solving this problem, the solution is obtained as shown inFIG. 9, for example, and it satisfies 100% of the fulfillment rate ofdemands from the marketing points. In this manner, it is possible toplan the production plan only with the restriction conditions and onemanagement index. However, since no consideration is made upon themanagement index other than the fulfillment rate of demands, forexample, the route of transporting from P1 to M2 by the airplane has thetransportation amount of 60, in spite the fact that the cost is 31(parts cost+production cost+transportation cost) for the sales 30. Forreferences, the profit produced by this production plan is 2,900, andthe inventory is 1,666.

[0290] As a second example (exercise 2) of the panning of a productionplan, there is listed up a method of planning and/or modifying theproduction plan, while watching the values of eight management indices,according to the steps shown in the FIG. 3.

[0291] <Step 301 (1^(st) time)>

[0292] The management indices are as below:

[0293] the fulfillment rate of demands is 100%, and

[0294] the profit is the maximum.

[0295] Herein, the planning and modification of the production plan areobtained by taking the management index of “the profit is the maximum”into the consideration, in addition to the management index of “thefulfillment rate of demands is 100%” indicated in the exercise 1.

[0296] <Step 302 (1^(st) time)>

[0297] The restriction conditions are, in addition to those 1 to 6,GV1=1 in the restriction condition 8, and GV6=1 in the restrictioncondition 13. The objective function is as follows, for example:

[0298] (Eq. 49) Objective function in the exercise 2, 1^(st) time${\min \quad \{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{-}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{-}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{-}}}} \}} + \{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{+}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{+}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{+}}}} \} + {10 \cdot d_{6}^{-}} - {10 \cdot d_{6}^{+}}$

[0299] When solving this problem, the solution is obtained as shown inFIG. 10, for example. The value of each of the management indices is asshown in FIG. 11. The profit is 3,110, being increased more than that ofthe prior example 1.

[0300] <Step 303 (1^(st) time)>

[0301] Studying the results, for making the profit maximal, the PC isproduced at P2 where the production cost is cheap, and is transported bymeans of the ship which is cheap in the transport cost. Due to therestriction on the operable time of the process of P2, a part of theoperation is conducted at P1, however the rate of operation at P1 islow, such as 41%. Also, it is transported via the ship, therefore theinventory is large, such as 1,678.

[0302] <Step 304>

[0303] Next, while maintaining the fulfillment rate of demands at 100%and the rate of operation at P1 and P2 are at 70%, minimization is triedon the money amount of the inventory. Namely, it is tried to bring themanagement indices as follows:

[0304] the fulfillment rate of demands is 100%,

[0305] the rate of operation is 70%, and

[0306] the inventory is minimal.

[0307] Herein, upon basis of the result of the first time, the planningand modification are conducted on the production plan, also by takinginto the consideration the management indices of “the rate of operationis 70%” and “the inventory is minimal”, in addition to that of “thefulfillment rate of demands is 100%”.

[0308] <Step 302 (2^(nd) time)>

[0309] The restriction conditions are, in addition to those 1 to 6,GV1=1 in the restriction condition 8, GV2=0.7 in the restrictioncondition 9, and GV8=1,600 in the restriction condition 15. Theobjective function is as follows, for example:

[0310] (Eq. 50) Objective function in the exercise 2, 1^(st) time${\min \quad \{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{-}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{-}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{-}}}} \}} + \{ {{45 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M1},{PC},t}^{+}}} + {30 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M2},{PC},t}^{+}}} + {35 \cdot {\sum\limits_{t = 1}^{T}d_{1,{M3},{PC},t}^{+}}}} \} + \{ {{0.7 \cdot d_{2,{P1}}^{-}} + {0.7 \cdot d_{2,{P2}}^{-}}} \} + \{ {{0.7 \cdot d_{2,{P1}}^{+}} + {0.7 \cdot d_{2,{P2}}^{+}}} \} + {10 \cdot d_{6}^{-}} - {10 \cdot d_{6}^{+}}$

[0311] When solving this problem, the solution is obtained as shown inFIG. 12, for example. The value of each the management indices is asshown in FIG. 13. The profit is reduced down to 2,826, comparing to thatof the first time, the inventory is also decreased down to 1,595, andthe rate of operation comes to 70%.

[0312] <Step 303 (2^(nd) time)>

[0313] Studying the results, for rising up the rate of operation at P1,the production amount at P2 is shifted to P1. Also, for decreasing downthe inventory, the transport means is shifted, stopping use of the shipwhich is long in the transportation lead time, to the airplane. In acase where the uncertainty is high in the demands, it can be the thatthe second time production plan is a superior plan. The planner of theproduction plan compares the first and second plans, by weighting dangerof conducting the production activity with holding much of inventory,danger of reducing the profit, and balance of the rate of operation,etc., in a balance, so as to find the superiority between them. Forexample, for avoiding the danger of inventory, the process is finishedas it is, or if the first one is better, it may be enough to set thesame target value to the first time or a new one in the step 304, andrecalculate it in the step 302.

[0314] As in the above, by setting the objective values of the pluralmanagement indices and repeating the steps 302 to 304 at least one ormore times, it is possible to plan the production plan by taking theplural management indices into the consideration.

[0315] In the step 303, as an example of the way of displaying themanagement indices on the display means, such as the CRT, etc., otherthan the format of the table as shown in FIG. 11, it may be depicted bythe radar chart as shown in FIG. 14, or by the rod graph as shown inFIG. 15, thereby displaying the management target values designated inthe step 301, such as, by a point 1401 or a line 1501. However, theFIGS. 14 and 15 show the results obtained from the first time of theexercise 2. In the radar chart, it is indicated, the larger the area ofa polygon 1402, and in the rod graph, the longer the rod, the better theindex. Therefore, with the indices, such as, the inventory, the cost,etc., being the smaller, the better, the display values of coordinatesare made larger in reverse proportion with the magnitude of the value.In this manner, indicating the management indices in the graph is a helpto understand the difference between the target values and the actualvalues and the relationship of the trade-off between the managementindices.

[0316] Also, when performing the steps 301 to 303 repetitively, it iseasy to grasp the comparison with the previous production plan, if thedifferences between the previous results are displayed, as shown inFIGS. 16 and 17. Broken line 1601 in the FIG. 16 indicates the result ofthe first time of the previous exercise 2, while the solid line 1602that of the second time of the previous exercise 2.

[0317] Also, displaying the result values at present or of the past (forexample, one day before, one month before, or one year before, etc.) inaddition thereto when displaying the radar chart or the graph, it ispossible to make them as reference values, in case of changing themanagement indices in planning of the production plan.

[0318] Also, in the embodiment mentioned above, the restrictioncondition of production capability and the restriction conditionsrelating to the target values of the management indices are accumulatedin a memory means (not shown in the figure). Also, the informationrelating to the transport of the parts and/or the products among theplural production points, supply points, and marketing points, and alsothe information relating to the costs at the plural points, etc., can beheld in the memory means (not shown in the figure). Also, under therestriction condition mentioned above, calculation for obtaining thesolution which achieve the target value of at least one of themanagement indices is executed by a calculation process means (not shownin the figure).

[0319] Also, the embodiment according to the present invention, whereinthe transport information among the plural points and/or the informationrelating to the cost, etc., at each of the points are transmitted fromthe user's terminal side via a network, while the solutions achievingthe target values of management indices are calculated out through thecalculation process in a production plan system which is accumulated ata host server side, thereby transmitting the processed results to theuser's terminals, or also other embodiment, wherein the information ofthe target values of management indices is transmitted from the user'sterminal side via the network, while the solutions achieving the targetvalues of management indices are calculated out through the calculationprocess in the production plan system accumulated at the host serverside, with using transport information among the plural points and/orthe information relating to the cost, etc., which are accumulated at thehost server side, thereby transmitting the processed results to theuser's terminals, falls within a region of the present invention.

[0320] According to the embodiment of the present invention, it ispossible to calculate out a feasible production plan, which satisfy thetarget values of plural management indices, quickly, when calculatingout the production amount, supply amount and/or transportation means ofthe plural products at the plural production/material supply/marketingpoints.

What is claimed is:
 1. A method of production planning, for calculatingout production amount and/or supply amount and/or transportation meansat a plural number of points of production, material supply and/ormarketing, comprising steps of: putting a relationship between a targetvalue of a predetermined management index and an estrangement valuetherefrom into restriction condition, when formulating the restrictioncondition into a linear programming problem; and calculating out afeasible production plan, so that the estrangement between saidpredetermined management index and the target value thereof, beingcalculated from an executable solution of said linear programmingproblem, comes to be minimal.
 2. A method of production planning, as isdefined in the claim 1 , wherein said management index is a combinationof at least one or more of inventory, profit, sales, cost, a rate ofoperation, fulfilling rate of demands from marketing point, cash whichproduction activity produces, and an efficiency at which the productionactivity produces the cash.
 3. A method of production planning, as isdefined in the claim 1 , wherein the target value of the managementindex is set to be equal to, greater or less than that, or maximal orminimal, with respect to a numerical value appointed.
 4. A method ofproduction planning, as is defined in the claim 1 , wherein theproduction amount and/or the supply amount and/or the transportationmeans is/are calculated out by repeating steps of: setting the targetvalue of the management index through an input means, solving saidlinear programming problem in a calculation means, displaying a resultthereof on a display means, and again, changing said restrictioncondition stored in a memory means upon receipt of change in the targetvalue of the management index through the input means, solving thelinear programming problem, the restriction condition of which ischanged, in the calculation means, and displaying the result thereof onthe display means.
 5. A memory medium, storing program for executingsaid processes, in the method of production planning, as defined in theclaim 1 .
 6. A method of production planning, for calculating outproduction amount and/or supply amount and/or transportation means at aplural number of points of production, material supply and/or marketing,comprising: a step of performing modeling process on a linearprogramming problem with using an equation between target values ofpredetermined management indices and estrangement values therefrom asrestriction condition; a step of calculating out the value of saidpredetermined management indices by solving said linear programmingproblem; and a step of calculating out a feasible production plan uponbasis of the value of said predetermined management indices.
 7. A methodof production planning, as defined in the claim 6 , wherein the linearprogramming problem is solved by adding at least one of managementindices to said predetermined management indices, or by changing atleast one of sad management indices into another index, or by changingat least one target value of said predetermined management indices intoanother value, thereby calculating out values of the management indicesafter the addition or the change thereof.
 8. A method of productionplanning, as defined in the claim 6 , wherein the values of saidpredetermined management indices are displayed on a display means in aform of a radar chart or a rod graph.
 9. A method of productionplanning, as defined in the claim 7 , wherein the values of saidpredetermined management indices and the values of said predeterminedmanagement indices after the addition or the change thereof aredisplayed on a display means in a form of a radar chart or a rod graph.10. A method of production planning, as defined in the claim 7 , whereinthe values of said predetermined management indices and actual values ofthe management indices are displayed on a display means in a form of aradar chart or a rod graph.
 11. A method of production planning,comprising: receiving at least one target value information ofmanagement indices which are transmitted from terminal sides of users;calculating out a solution for achieving the target values of themanagement indices or a solution for making estrangement from targetvalues of the management indices minimal, through conducting calculationprocess in a production plan system which is accumulated at a hostserver side, with using transportation information among a plural numberof points and/or information relating to cost at each point, which areaccumulated in said server side.